The genius of Euler : reflections on his life and work

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The genius of Euler : reflections on his life and work

edited by William Dunham

（MAA tercentenary Euler celebration, v. 2）（MAA spectrum）

Mathematical Association of America, c2007

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

Celebrating the 300th birthday of Leonhard Euler (1707-1783), one of the brightest stars in the mathematical firmament, this book stands as a testimonial to a mathematician of unsurpassed insight, industry, and ingenuity. The collected articles, aimed at a mathematically literate audience, address aspects of Euler's life and work, from the biographical to the historical to the mathematical. The oldest of these was written in 1872, and the most recent dates to 2006. Some of the papers focus on Euler and his world, others describe a specific Eulerian achievement, and still others survey a branch of mathematics to which Euler contributed significantly. Among the 34 contributors are some of the most illustrious mathematicians and mathematics historians of the past century, e.g. Florian Cajori, Carl Boyer, George Polya, Andre Weil, and Paul Erdoes. And there are a few poems and a mnemonic just for fun.

目次

  • Acknowledgments
  • Preface
  • About the authors
  • Part I. Biography and Background: 1. Introduction to Part I
  • 2. Leonhard Euler B. F. Finkel
  • 3. Leonhard Euler, supreme geometer (abridged) C. Truesdell
  • 4. Euler (abridged) Andre Weil
  • 5. Frederick the Great on mathematics and mathematicians (abridged) Florian Cajori
  • 6. The Euler-Diderot anecdote B. H. Brown
  • 7. Ars expositionis: Euler as writer and teacher G. L. Alexanderson
  • 8. The foremost textbook of modern times Carl Boyer
  • 9. Leonhard Euler, 1707-1783 J. J. Burckhardt
  • 10. Euler's output, a historical note W. W. Rouse Ball
  • 11. Discoveries (a poem) Marta Sved and Dave Logothetti
  • 12. Bell's conjecture (a poem) J. D. Memory
  • 13. A response to 'Bell's conjecture' (a poem) Charlie Marion and William Dunham
  • Part II. Mathematics: 14. Introduction to Part II
  • 15. Euler and infinite series Morris Kline
  • 16. Euler and the zeta function Raymond Ayoub
  • 17. Addendum to 'Euler and the Zeta Function' A. G. Howson
  • 18. Euler subdues a very obstreperous series (abridged) E. J. Barbeau
  • 19. On the history of Euler's constant J. W. L. Glaisher
  • 20. A mnemonic for Euler's constant Morgan Ward
  • 21. Euler and differentials Anthony Ferzola
  • 22. Leonhard Euler's integral: a historical profile of the gamma function Philip Davis
  • 23. Change of variables in multiple integrals: Euler to Cartan Victor Katz
  • 24. Euler's vision of a general partial differential calculus for a generalized kind of function Jesper Lutzen
  • 25. On the calculus of variations and its major influences on the mathematics of the first half of our century Erwin Kreyszig
  • 26. Some remarks and problems in number theory related to the work of Euler Paul Erdoes and Underwood Dudley
  • 27. Euler's pentagonal number theorem George Andrews
  • 28. Euler and quadratic reciprocity Harold Edwards
  • 29. Euler and the fundamental theorem of algebra William Dunham
  • 30. Guessing and proving George Polya
  • 31. The truth about Koenigsberg Brian Hopkins and Robin Wilson
  • 32. Graeco-Latin squares and a mistaken conjecture of Euler Dominic Klyve and Lee Stemkoski
  • Glossary Schattschneider et. al.
  • About the editor.

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